Analog computer for simultaneous equations



July 17, 1956 E. w. slLvER'rooTl-l ANALOG COMPUTER FOR SIMULTANEOUS EQUATIONS Filed March l, 1951 4 Sheets-Sheet l 'U' OWN 'LI-I Pfl-I 072835' A A n A aff ATTORN EY 4 Sheets-Sheet 2 E. W. SILVERTOOTH ANALOG COMPUTER FOR SIMULTANEOUS EQUATIONS July 17, 1956 Filed March l,

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ATTORNEY July 17, 1956 E. w. slLvx-:RTooTH ANALOG COMPUTER FOR SIMULTANEOUS EQUATIONS 4 Sheets-Sheet 3 Filed March l, 1951 SYM ATTORNEY E. W. SILVERTOOTH ANALOG COMPUTER FOR SIMULTANEOUS EQUATIONS July 17, 1956 Filed March l, 1951 4 Sheets-Sheet 4 raw ATTORNEY 2,755,021 Patented July 17, 1956 United States Patent Otice ANALGG COMPUTER FOR SIMULTANEOUS EQUATIONS y Application March 1, 1951, Serial No. 213,454`

7 Claims. (Cl. 23S-61) The present invention relates to computers of the analog type and more particularly to a computer adapted for the solution of simultaneous equations of a particular type.

An example of the type of simultaneous equations for the solution of which the present computer is designed is found in the production control of alloy quality. To correct the composition of an alloy, analysis of the alloy must be made very rapidly so that it can be corrected if in error while the melt is still in the crucible. For the purpose of effecting such analysis, direct reading spectrometers havel been developed by which an accurate quantitative analysis of at least eight elements in an alloy can be obtained in forty-five seconds. Such a spectrometer is described in an article entitled Direct-reading spectrometer for ferrous analysis in the Journal of the Optical Society of America, volume 37, No. 9, pages 707 to 713, September 1947.

For. most applications it is satisfactory to read the dials of such an instrument directly in percent concentration of the indicated elements. However, the fact that such dials really indicate apparent rather than true concentration of the respective elements (apparent concentration being the concentration an alloying element appears to have if it is assumed that the matrix element concentration is one hundred percent) makes necessary a series of computations for the purpose of obtaining true concentration ofthe alloying elements in the case of high alloys such as stainless steel and the like containing a relatively high concentration of minor components and in which it is desired to maintain a close control of the true concentration of such components. 'I'his computation requires the solution of the following system of equations:

where Ak=`apparent concentration of alloy component k asv indicated by direct-reading spectrometer. X k-` -true concentration of alloy component k.- S=true concentration of matrix component. n=total number of alloy components, all concentrations I being expressed in percentages.

J y which approximatesa true logarithmic response by giving a.

The solution of these equations is accomplished by the computer of the present invention irst, by adding together voltages representative of each ,of a series of apparent concentrations indicated by the direct-reading spectrometer; adding to the sum thereof a voltage representative of the constant and feeding the total voltage thus obtained to the winding of a balancing potentiometer. A voltage representative of any single selected apparent concentration is simultaneously fed to the slider of the balancing potentiometer through an amplifier controlling a servo-motor actuator for the slider so that the servomotor will stop only when the voltages fed to the potentiometer winding and the slider, respectively, balance. An indicator actuated by the servo-motor as it positions the slider of the potentiometer exhibits the true concentration of the element, the apparent concentration of which was selected for feeding to the potentiometer slider.

In using the computer of the present invention it is necessary only for the operator to read the dials of the direct-reading spectrometer, set the readings obtained. into the computer of the present invention, and then push in succession ,one button for each element, after which he reads the true concentration of the element represented by the button pushed on the indicator of the computer. An additional button is provided which causes the indicator to bre positioned to exhibit the concentration of the matrix element.

The preferred embodiment of the present invention will be best understood by reference to the following detailed description thereof and to the accompanying drawings, in which:

Figure la, lb, lc and ld are complemental sections of a circuit diagram of a computer embodying the invention.

Referring to Figure la, the computer is powered byv a power transformer 10 having a primary winding 11 connected across the power line 12 through an onand oit-switch 13. An indicating pilot light 14 is connected across the primary 11 and one condenser 15 to ground is provided in each leg of the primary winding.

The power transformer 10 is provided with a plurality of secondary windings. Winding 17 is provided for the purpose of supplying current to the heaters of the various tubes employed in the computer. Winding 18 supplies power to the cathode of a full wave rectifier tube 19; while winding 20 supplies power to the plates of said tube. Winding 25 supplies power to the potentiometer circuit of the computer; one side thereof being at ground potential as indicated at 26.

The potentiometer circuit consisting of leads 30 and 31 powered by secondary winding 25, as above described, is shunted by eight input potentiometers 32 to 39, respectively. The sliders 32a to 39a, respectively, of these potentiometers are adapted to be adjusted to positions representative of the various apparent concentrations indicated by the direct reading spectrometer, and since these apparent concentrations may vary from a fraction of one percent to a value in excess of 100 percent, it is desirable to arrange the potentiometers 32 to 39 in groups conveniently adapted to handle various ranges of percentages. Therefore, as illustrated, the potentiometers 32 and 33 are adapted to be set to represent percentages' of from zero to one percent apparent concentration of the elements represented by them; the potentiometers 34 to 37, inclusive, are adapted to be adjusted to represent concentrations of from zero to ten percent of the respective elements represented by them, and the potentiometers 38 and 39 are adapted to be adjusted to represent percentages of from zero to per cent of the respective elements represented by them.

The output voltages of each of the potentiometers 32 to 37, inclusive, is `shunted by a dividing network 40 linear approximation to a logarithmic curve for each decade of the range covered by the computer. Accuracy is further enhanced by the provision of high impedance resistor 43 in connection with each of the potentiometers 32 to 39, inclusive; certain of the latter being shunted by resistors 44 where necessary.

By the arrangement just described voltages proportionate to the several apparent concentrations of alloy components to which the sliders of potentiometers 32 to 39, inclusive, have been set are fed into the lines to 57, inclusive. The constant term 100 determined by resistor 58 is fed through line 59 and the voltages of lines 50 to 57 and 59 are added together by means of resistors 42 and fed to the amplifier illustrated in Figure lc.

This amplifier is a constant gain amplifier comprising a high gain amplifier with negative feed-back over three stages which effects a 180 phase reversal at the carrier frequency, so that its output will be opposite in phase to the second circuit signal hereinafter referred to and so as to provide a match to the lower impedance of the potentiometer hereinafter described by which balancing is effected.

Essentially, the amplifier of Figure lc comprises three low frequency compensatingnetworks 65, and 75,` and one high frequency compensating network which control the phase shift characteristics of the amplifier and are required due to the large amount of feed-back necessary to make operation of the amplifier stable. Also in order to preserve stability, the plate supply of this amplifier instead of being taken directly from the filtered rectifier output has introduced therein a stabilizer circuit generally designated (Figure la) which comprises a conventional electronic regulator using, for example, 6SJ7GT and 6AS7G tubes and a voltage regulator tube OC3..

The output of the amplifier of Figure lc is fed to the winding of a balancing potentiometer 90, adjustment of the slider a of which is adapted to match the output of this amplifier with the voltage fed to line 91 as a second circuit, for any of a series of pushbutton switches 92 to 99, inclusive` adapted to connect line 91 with any of the lines 50 to 57, inclusive, respectively; resistors as indicated being interposed in the respective lines both to effect the proper balancing relationships and as safety factors to protect the instrument in the case of the simultaneous depression of more than one of the buttons 92 to 99, inclusive. Whenever the voltage being fed out of the amplifier of Figure lc to the winding of potentiometer 90 differs from the voltage being fed into line 91 from the pushbuttons 92 to 99, inclusive, a phase sensitive error signal is fed into the input of a servo-amplifier (Figure ld) which, as illustrated, l

consists of two 6SL7GTs in cascade and two 6V6GTS. The output of the servo-amplifier 100 is fed to a servomotor (Figure ld), the field winding of which is connected through a switch 13 tothe power line 12, as shown,

and the rotor of which is mechanically connected tothe slider 90u` of potentiometer 90 so that operation of the servo-motor 105 willposition slider 90a in the proper direction and to the proper extent to equalize the voltage fed to thc input of the servo-amplifier 100. An indicator also connected to the rotor of the servo-motor 105 is appropriately calibratedV to give the desired true concentration of the alloying element represented by the one of the pushbuttons 92 to 99'thc depression of which initiated the operation of the servo-motor.

ln the same manner an additional pushbutton may be provided to connect line 59, with line 91 and thereby cause indicator lltlto display the true concentration of the matrix component of thealloy.

Throughout the circuit diagram illustrated in the accompanying drawings, legends have been placed adjacent the notenticmeter. windings and other resistorsA and adjacent other electrical components indicating the values thereforiwhich. have been found preferable in an' actual embodiment ofrtheinvention. Itl will be apparent to those skilletdrin` the i art',4 however, that thesevalues are purelyf illustrative and that equivalents may be readily substituted in accordance with conventional practices.

In operation the operator firsts adjusts the sliders of the potentiometers 32 to 39, inclusive, to positions representative of the apparent concentrations of alloy constituents as read from the spectrophotometer. Constituents in which the apparent concentration is less than one percent are set up on the potentiometers 32 and 33. Constituents the apparent concentration of which is less than ten percent but more than one percent are set up on the potentiometers 34, 35, 36 and 37. Constituents the apparent concentration of which is more than ten percent but less than percent are set up on potentiometers 38 and 39. Any of these potentiometers may be left at zero Without affecting the accuracy of the result of the computation, so that while the present computer is designed to handle computations relating to alloys having up to eight constituents, it can also handle alloys containing any lesser numbers of constituents.

After adjusting the potentiometers 32 to 39 in this way, the master switch 13 being closed, the operator has only to close the button switches 92 to 99, inclusive, successively. Upon closure of each switch the servo-motor 105 will actuate the indicator 110, and when it cornes to rest it will display the true concentration of the alloy constituent represented by the button switch which has been closed. Similarly, the true concentration of the matrix constituent of the alloy may bc computed by closing the button switch 115.

What is claimed is:

1. In an electrical analog computer of the character described, a potentiometer circuit including a plurality of input potentiometers each having a winding in shunt in. said circuit and an input slider operatively associated with said winding and adjustable with respect thereto to produce a potentiometer output voltage proportional to the value of an equation term, means for adding said output voltages comprising a common lead connecting said plurality of input sliders, means for balancing a first factor including a selected one of said input potentiometer output voltages with a second factor including the sum of the output voltages of all of said input potentiometers cornprising a balancing potentiometer having a balancing winding the potential of which is responsive to variations in the potential of said common lead, and an adjustable balancing slideroperatively associated with said balancing winding, switching means for selectively connecting said' balancing slider with any one of said input sliders, and means for indicating when said balancing slider is adjusted to a position in which the said first factor balances saicl` second factor.

2. In an electrical analog computer of ythe character described, a potentiometer circuit including a plurality of input potentiometers each having a winding in shunt in said circuit and an input slider operatively associated with said winding and adjustable with respect thereto to` produce a potentiometer output voltage proportional to the value of an equation term, means for addingl said output voltages comprising. -a common lead connecting said plurality of input sliders, meansfor balancing a dist factor including a selected one of said input potentiometer output voltages with a. second factor including the sum of the output voltages of all ofV said input potentiometers comprising a balancingY potentiometer having a balancing winding the potential of which is responsive toV variations in thefpotential of' said common lead, and an adjustable balancing slider operatively associated with said balancing winding; switching means for selectively connecting said balancing slider with any one of said input sliders, motor operated means for effecting adjustment of said balancing slider, and control means for said motor operated means responsive to an error signal voltage in the connection betweant said balancing slider and any one ofi said input sliders connected thereto through lsaid switching means.

3. In an electrical analog computer arranged for the non-iterative solution of simultaneous equations, the combination of a plurality of potentiometer windings having dierent lorders of resistance arranged to permit the insertion of input values and the continuous flow of current thereth-ru, means for selecting from said windings potentials proportional to the values of desired input quantities; means for protecting said windings from overload currents, 4said means constituting a portion of the potential select-ing means; compensating network means .associated with each of said means for selecting potentials; a power supply; high gain amplifying means, having negati-ve feedback :and a plurality of stages providing unity gain amplification independent of variations in the frequency and voltage of said power supply and reversal of phase in the output thereof; means for adding outputs from said network means and transmitting such added values to said high gain amplifying means; differential amplifying means, and means for individually applying any one of said selected potentials -to said differential amplifying means; a ma-tchingpotentiometer, motor means for driving said matching potentiometer, and a power amplifier tar-ranged to drive said motor means; said differential amplifying means being arranged to adjust said matching potentiometer to equate the` individually applied one of said selected potentials proportionally with the phase-reversed unity gain output of said ihigh gain amplifying means, and means for indieating the proportionality between the potentials so equated.

4. An electrical analog computer arranged for the noniterative solution of simultaneous equations, comprising a plurality of potentiometer windings of various resistances 'ar-ranged to permit the :continuous flow of current therethrough, means for selecting from said windings potentials proportional to the values of desired input quantities, means constituting a portion 4of the potential selec-ting means for limiting currents `through said windings whi-le permitting Icontinuous flow thereof; compensating network means associated with each of said mear-s for selecting potenti-als; power supply means; amplifying means independent of variations in the frequency and voltage furnished by said power supply means, and arranged to provide an output of opposite sense; means for adding potential outputs from said network means and transmitting such added output potentials values to said amplifying means; potentiometer means, means for applying the output of said amplifying means Ito said potentiometer means, means for summing any one of said potentials proportional to the values `of desired input quantities and the potential output of said potentiometer; means for driving said potentiometer until the combination with said summing potentials is zero; and means for indicating the :amount of movement occurring Iin said potentiometer means while 'being driven 'to a vbalanced position.

5. In an electrical -analog computer arranged for .the

non-iterative solution of simultaneous equations, the combination of an alternating current source, a plurality of potentiometer windings energized thereby, means for selecting from each of said potentiometers potentials corresponding to desired input values, means f-or adding said potentials to obtain a value proportional to the sum of the potentials so selected, a balancing potentiometer, means for applying the potential representative of said sum to said balancing potentiometer, means for selectively obtaining one of said input potentials, a servo amplifier, means for amplifying a selected one of said input potentials and the output potential of `said balancing potentiometer in phase opposition to the input of said servo amplilier, and means actuated by said servo amplifier to adjust said potentiometer to a balanced position.

6. An electrical analog computer arranged for the noniterative solution of simultaneous equations, comprising an alternating current source, a plurali-ty of potentiometers energized thereby, each of said potentiometers being .adjustable to provide individual output potentials corresponding to respective ones of 'a plurality of selected input values; summation means for obtaining a potential equivalent to the sum of said output potentials, means for reversing the phase of said summation potential, a potentiometer having said reversed phase summation potential applied thereacr-oss, a servo amplier having its input connected to a movable contact on said last men- -tioned potentiometer, means for selectively applying individual ones of said output potentials to the input of said servo amplifier, and means operated by the output of said servo amplifier for adjusting said movable contact to produce a balance potential at :the input of said servo amplifier.

7. In an electrical analog compu-ter arranged for rthe non-iterative solution of simultaneous equations, an alternating current source; a plurality of potentiometers energized thereby, and adjustable to provide output potentials corresponding individually to selected input values; means for obtaining continuously a potential representat-ive of the sum of said output potentials, a balancing potentiometer having an adjustable contact, :a differential servo ampliiier 'having its input connected to said contact; means for selectively applying a potential from one of said plurality of potentiometers to the input of said servo :amp-liner; and means operated by .the output of said servo amplifier for adjusting said balancing potentiometer.

References Cited in the le of this patent UNITED STATES PATENTS 2,443,098 Dean June 8, 1948 2,454,520 Moore Nov. 23, 1948 2,468,150 Wilcox Apr. 26, 1949 2,502,308 Brunn Mar. 28, 1950 2,503,387 Hartwig Apr. 11, 1950 2,543,650 Walker =Feb. 27, 1951 2,584,809 Oberlin Feb. 5, 1952 OTHER REFERENCES Radio Engineers Handbook, F. E. Terman; McGraw- Hill, 1943; page 905, Fig. 6, and page 949, Fig. 56(a).

'Electronic Computers, William Shannon; Electronics, August 1946; pp. -113; Fig. 3.

Bridge Type Electrical Computers, W. K. Ergen, The Review of Scientific Instruments; vol. 18, No. 8, August 1947; pp. 564-567.

Electronic Instruments, Greenwood, Jr. et al.; McGraw- Hill, 1948; page 56, Fig. 3.15; page 440, Fig. 12.56; page 149, Fig. 6.14; page 139, Fig. 6.7; page 125, Fig. 5.36 and Sec. 5:4. 

